A computational approach to statistics by Klotz J.H.

By Klotz J.H.

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Extra resources for A computational approach to statistics

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Then the sample space is finite with S = {HHH, HHT, HT H, T HH, HT T, T HT, T T H, T T T }. For another example, consider the random experiment of tossing a coin repeatedly until a heads (H) come up. Then the sample space is countably infinite with S = {H, T H, T T H, T T T H, . }. 2 CHAPTER 2. DISCRETE PROBABILITY Events Events are subsets of the sample space and we often use letters A, B, C, etc. to label them. For example in the finite sample space for the toss of a coin 3 times we might consider the event A = {HHT, HT H, T HH} that 2 heads came up in 3 tosses.

17 larger than the population incidence. So don’t panic but follow it up. 1 Independent Events For the case when P (A|B) = P (A), that is knowing B has occurred does not affect the probability of A, we say that the events A and B are independent. This condition can also be written P (A ∩ B) = P (A)P (B) for A and B independent. We say the events {A1 , A2 , . . , An } are pairwise independent if P (Ai ∩ Aj ) = P (Ai )P (Aj ) for all i, j with i = j. We say the events {A1 , A2 , . . , An } are mutually independent if we have jk jk P (Ai ) for j1 < j2 < .

What is the probability that the person has the disease? Let B1 be the event that the person has the disease, B2 that the person does not, and A the event of being positive for the disease on the screening test. 0001 . 001917 . 17 larger than the population incidence. So don’t panic but follow it up. 1 Independent Events For the case when P (A|B) = P (A), that is knowing B has occurred does not affect the probability of A, we say that the events A and B are independent. This condition can also be written P (A ∩ B) = P (A)P (B) for A and B independent.

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